THEORETICAL ELEMENTS OF ELECTRICAL ENGINEERING
CONTENTS PROJECT PORTFOLIO ANALYSIS OF A POWER DELIVERY SYSTEM CYLINDRICAL TYPE TRANSMISSION LINES DC TRANSDUCER DETERMINATION OF THE CONDUCTIVITY OF A CIRCULAR CONDUCTING DISK DIRECTIONAL COUPLER ANALYSIS ILL-DEFINED GROUNDING PROBLEMS INDUCTION MACHINE ANALYSIS LINE-MATCHING TECHNIQUE USING AN EXPONENTIAL TRANSMISSION-LINE SECTION LINEAR VARIABLE DIFFERENTIAL TRANSFORMER MAGNETIC ACTUATOR AND SENSOR DEVICE OVERHEAD-LINE PROTECTION BY GROUND WIRES POWER LINE CARRIER COMMUNICATION PSEUDO-BALANCED THREE-PHASE LINES SCREENED HIGH-VOLTAGE THREE-PHASE INSTALLATION SHIELDED THREE-PHASE CABLE ANALYSIS THREE-ROUTE MICROWAVE SPLITTER TRANSMISSION-LINE SYSTEM WITH BALUN TRANSFORMER FOR EVEN- TO ODD-MODE CONVERSION TRANSMISSION-LINE SYSTEM WITH TRANSFORMER-STAGE MATCHING TWO-WAY LOUDSPEAKER ANALYSIS VARIABLE RELUCTANCE TRANSFORMER CONTENTS PART I A BRIEF OVERVIEW INTRODUCTION BASIC FIELD VECTORS THE ELECTRIC AND MAGNETIC FIELD VECTORS CONSTITUTIVE RELATIONS UNITS AND NOTATION FUNDAMENTAL CONCEPTS OF VOLTAGE AND CURRENT INTENSITY PART II STATIONARY FIELD PHENOMENA ELECTROSTATICS FUNDAMENTAL EQUATIONS GRADIENT ELECTRIC FIELD, ELECTRIC POTENTIAL, VOLTAGE, KIRCHHOFF’S VOLTAGE LAW ELECTRIC CHARGE, ELECTRIC DISPLACEMENT VECTOR DIELECTRIC MEDIA, PERMITTIVITY, POLARIZATION, DIELECTRIC STRENGTH CONDUCTORS IN ELECTROSTATIC EQUILIBRIUM APPLICATION EXAMPLE (FILAMENT OF CHARGE) CAPACITOR, CAPACITANCE, ELECTRIC ENERGY APPLICATION EXAMPLE (TWO-WIRE TRANSMISSION LINE) MULTIPLE CONDUCTOR SYSTEMS 2 9 1 CAPACITANCE MATRIX 2 9 2 PARTIAL CAPACITANCES SCHEME 2 10 APPLICATION EXAMPLE (ELECTRIC COUPLING IN PRINTED CIRCUIT BOARDS) 2 11 ELECTRIC FORCES AND TORQUES 2 12 PROPOSED HOMEWORK PROBLEMS STATIONARY CURRENTS CONDUCTIVITY, CURRENT DENSITY, ELECTRIC CIRCUITS CURRENT INTENSITY, KIRCHHOFF’S CURRENT LAW RESISTOR, CONDUCTANCE, RESISTANCE, OHM’S LAW APPLICATION EXAMPLE (THE POTENTIOMETER) APPLICATION EXAMPLE (THE WHEATSTONE BRIDGE) JOULE LOSSES, GENERATOR APPLIED FIELD GENERATOR ELECTROMOTIVE FORCE, POWER BALANCE PROPOSED HOMEWORK PROBLEMS MAGNETIC FIELD OF STATIONARY CURRENTS AMPÈRE’S LAW, MAGNETOMOTIVE FORCE, MAGNETIC VOLTAGE MAGNETIC INDUCTION FIELD, MAGNETIC INDUCTION FLUX APPLICATION EXAMPLE (POWER LINE MAGNETIC FIELDS) MAGNETIC MATERIALS, FERROMAGNETIC MEDIA, SATURATION AND HYSTERESIS MAGNETIC CIRCUITS APPLICATION EXAMPLE (THREE-LEGGED TRANSFORMER) MAGNETIC RELUCTANCE INDUCTOR, INDUCTANCE, MAGNETIC FLUX LINKAGE, MAGNETIC ENERGY 4 10 APPLICATION EXAMPLE (COAXIAL CABLE) CONTENTS 4 11 HYSTERESIS LOSSES 4 12 MULTIPLE CIRCUIT SYSTEMS 4 13 MAGNETIC FORCES AND TORQUES 4 14 APPLICATION EXAMPLE (U-SHAPED ELECTROMAGNET) 4 15 PROPOSED HOMEWORK PROBLEMS PART III SLOW TIME-VARYING FIELDS MAGNETIC INDUCTION PHENOMENA GRADIENT AND INDUCTION ELECTRIC FIELDS, POTENTIAL VECTOR REVISITING THE VOLTAGE CONCEPT INDUCTION LAW APPLICATION EXAMPLE (MAGNETIC NOISE EFFECTS) VOLTAGES AND CURRENTS IN MAGNETICALLY MULTICOUPLED SYSTEMS APPLICATION EXAMPLE (MAGNETIC COUPLING IN PRINTED CIRCUIT BOARDS) EDDY CURRENTS GENERALIZATION OF THE INDUCTION LAW TO MOVING CIRCUIT SYSTEMS 5 10 APPLICATION EXAMPLE (ELECTROMECHANICAL ENERGY CONVERSION) 5 11 DC VOLTAGE GENERATION 5 12 AC VOLTAGE GENERATION 5 13 PROPOSED HOMEWORK PROBLEMS ELECTRIC INDUCTION PHENOMENA DISPLACEMENT CURRENT, GENERALIZED AMPÈRE’S LAW CHARGE CONTINUITY EQUATION REVISITING THE CURRENT INTENSITY CONCEPT APPLICATION EXAMPLE (CAPACITOR SELF-DISCHARGE) VOLTAGES AND CURRENTS IN ELECTRICALLY MULTICOUPLED SYSTEMS LUMPED PARAMETERS CIRCUIT ANALYSIS STEADY-STATE HARMONIC REGIMES 7 2 1 CHARACTERIZATION OF SINUSOIDAL QUANTITIES 7 2 2 COMPLEX AMPLITUDES OR PHASORS 7 2 3 APPLICATION EXAMPLE (RLC CIRCUIT) 7 2 4 INSTANTANEOUS POWER, ACTIVE POWER, POWER BALANCE EQUATION 7 2 5 COMPLEX POWER, COMPLEX POYNTING THEOREM 7 2 6 IMPEDANCE AND ADMITTANCE OPERATORS 7 2 7 RESONANCE 7 2 8 APPLICATION EXAMPLE (RL C CIRCUIT) TRANSFORMER ANALYSIS 7 3 1 THE IDEAL TRANSFORMER 7 3 2 TRANSFORMER IMPEDANCE, PSEUDO LENZ’S LAW 7 3 3 EQUIVALENT CIRCUITS 7 3 4 APPLICATION EXAMPLE (CAPACITIVELY LOADED TRANSFORMER) TRANSIENT REGIMES 7 4 1 FREE-REGIME AND STEADY-STATE SOLUTIONS 7 4 2 INITIAL CONDITIONS 7 4 3 ANALYSIS OF THE CAPACITOR CHARGING PROCESS 7 4 4 CONNECTING AN INDUCTIVE LOAD TO AN AC GENERATOR 7 4 5 DISCONNECTING AN INDUCTIVE LOAD 7 4 6 APPLICATION EXAMPLE (SWITCHING OFF A TRANSFORMER PROTECTED BY A CAPACITOR) PART IV RAPID TIME-VARYING FIELDS ELECTROMAGNETIC FIELD PHENOMENA ELECTROMAGNETIC WAVES POYNTING THEOREM, POYNTING VECTOR, POWER FLOW TIME-HARMONIC FIELDS, FIELD POLARIZATION, RMS FIELD VALUES PHASOR-DOMAIN MAXWELL’S EQUATIONS, MATERIAL MEDIA CONSTITUTIVE RELATIONS APPLICATION EXAMPLE (UNIFORM PLANE WAVES) COMPLEX POYNTING VECTOR APPLICATION EXAMPLE (SKIN EFFECT) TRANSMISSION-LINE ANALYSIS TIME-DOMAIN TRANSMISSION-LINE EQUATIONS FOR LOSSLESS LINES 9 2 1 WAVE PARAMETERS, PROPAGATION VELOCITY, CHARACTERISTIC WAVE RESISTANCE 9 2 2 PULSE PROPAGATION, PULSE REFLECTION APPLICATION EXAMPLE (PARALLEL-PLATE TRANSMISSION LINE) FREQUENCY-DOMAIN TRANSMISSION-LINE EQUATIONS FOR LOSSY LINES 9 4 1 PER-UNIT-LENGTH LONGITUDINAL IMPEDANCE, PER-UNIT-LENGTH TRANSVERSE ADMITTANCE 9 4 2 PROPAGATION CONSTANT, PHASE VELOCITY, CHARACTERISTIC WAVE IMPEDANCE 9 4 3 TRANSFER MATRIX, NON-UNIFORM LINE ANALYSIS FREQUENCY-DOMAIN TRANSMISSION-LINE EQUATIONS FOR LOSSLESS LINES 9 5 1 TERMINATED LINE, LOAD REFLECTION COEFFICIENT, LINE INPUT IMPEDANCE 9 5 2 MATCHED LINE, OPEN LINE, SHORT-CIRCUITED LINE 9 5 3 STANDING WAVE PATTERN, STANDING WAVE RATIO, ACTIVE POWER 9 5 4 THE LOW-FREQUENCY LIMIT CASE, SHORT LINES APPLICATION EXAMPLE (LINE-MATCHING TECHNIQUES) MULTICONDUCTOR TRANSMISSION LINES APPLICATION EXAMPLE (EVEN AND ODD MODES) PROJECT PORTFOLIO THIS PROJECT PORTFOLIO – PLACED HERE AT THE BEGINNING OF THE BOOK – IS A TEASER AIMED AT TRIGGERING YOUR CURIOSITY ABOUT THE SUBJECTS TO BE DEVELOPED THROUGHOUT THE BOOK THE PORTFOLIO IS INTENDED TO BE A KEY TOOL FOR ASSESSING THE SKILLS AND KNOWLEDGE THAT YOU SHOULD ACQUIRE AFTER COMPLETING THE READING, UNDERSTANDING AND COMPREHENDING OF THE CONTENTS OF THIS BOOK THE PORTFOLIO INCLUDES A SERIES OF 20 FINAL-YEAR PROJECTS WHICH TIE TOGETHER AND INTERLINK THE MANY SUBJECTS THAT YOU ARE GOING TO LEARN AND HEAR ABOUT DURING THIS SEMESTER WHILE SOME PROJECTS ARE MORE FOCUSED ON A SPECIFIC THEME, OTHERS (MOST OF THEM) ENCOMPASS AND MIX SEVERAL TOPICS FROM SEVERAL CHAPTERS THE MAIN OBJECTIVE IS TO PROVIDE YOU WITH AN INTEGRATED GLOBAL VIEW OF THE MANY ASPECTS DEALT WITH IN THE BOOK, AIMING TO EMPOWER YOU WITH A SOUND AND LASTING GRASP OF THE ELECTROMAGNETIC FOUNDATIONS OF ELECTRICAL ENGINEERING IT IS ABSOLUTELY AMAZING HOW A SET OF ONLY FOUR EQUATIONS – MAXWELL’S EQUATIONS – CAN BE SO FRUITFUL AS FAR AS THEIR RANGE OF APPLICATIONS IS CONCERNED IN FACT, THE SAME BASIC TOOL WILL ALLOW YOU TO ANALYZE A HUGE VARIETY OF ELECTROMAGNETIC PHENOMENA AND ELECTRICAL ENGINEERING DEVICES AND SYSTEMS IN THIS PORTFOLIO YOU WILL BE FACED WITH REAL-LIFE ENGINEERING SUBJECTS SUCH AS ROTATING INDUCTION MACHINES, SOUND COLUMNS, MICROWAVE POWER SPLITTERS, AND MUCH MORE A LIST OF THE PROPOSED PROJECTS FOLLOWS THEIR SEQUENCE IS PURELY ALPHABETICAL IN ORDER TO AVOID ANY UNSUBSTANTIATED CLUES NOT ONLY ON THE IMPORTANCE OF THE PROPOSED THEMES, BUT ALSO ABOUT THEIR INTRINSIC DIFFICULTIES PROJECT ANALYSIS OF A POWER DELIVERY SYSTEM PROJECT CYLINDRICAL TYPE TRANSMISSION LINES PROJECT DC TRANSDUCER PROJECT DETERMINATION OF THE CONDUCTIVITY OF A CIRCULAR CONDUCTING DISK PROJECT DIRECTIONAL COUPLER ANALYSIS PROJECT ILL-DEFINED GROUNDING PROBLEMS PROJECT INDUCTION MACHINE ANALYSIS PROJECT LINE-MATCHING TECHNIQUE USING AN EXPONENTIAL TRANSMISSION-LINE SECTION PROJECT PORTFOLIO PROJECT LINEAR VARIABLE DIFFERENTIAL TRANSFORMER PROJECT MAGNETIC ACTUATOR AND SENSOR DEVICE PROJECT OVERHEAD-LINE PROTECTION BY GROUND WIRES PROJECT POWER LINE CARRIER COMMUNICATION PROJECT PSEUDO-BALANCED THREE-PHASE LINES PROJECT SCREENED HIGH-VOLTAGE THREE-PHASE INSTALLATION PROJECT SHIELDED THREE-PHASE CABLE ANALYSIS PROJECT THREE-ROUTE MICROWAVE SPLITTER PROJECT TRANSMISSION-LINE SYSTEM WITH BALUN TRANSFORMER FOR EVEN- TO ODD-MODE CONVERSION PROJECT TRANSMISSION-LINE SYSTEM WITH TRANSFORMER-STAGE MATCHING PROJECT TWO-WAY LOUDSPEAKER ANALYSIS PROJECT POWER DELIVERY SYSTEM COMPRISING A VOLTAGE GENERATOR, A TRANSMISSION LINE AND THREE INDUSTRIAL CONSUMERS THE TRANSMISSION LINE, REPRESENTED BY ITS SIMPLIFIED LOW-FREQUENCY EQUIVALENT MODEL, IS CHARACTERIZED BY THE FOLLOWING PARAMETERS: LENGTH: 200 KM; PER-UNIT-LENGTH RESISTANCE: 02 /KM; PER-UNIT-LENGTH REACTANCE: 10 /KM ˜ GRAPHICAL PLOT OF THE INSTANTANEOUS POWER AGAINST TIME, PKT, FOR K = 1 2 A CAPACITOR IS PLACED AT THE FAR END OF THE LINE FOR POWER FACTOR COMPENSATION PURPOSES PROJECT PORTFOLIO